-560.114 a rational or irrational

In the polar coordinate system, the region R corresponds to 0 ≤ r ≤ (2 - 9sin(θ))/(9cos(θ) + 9sin(θ)) and 0 ≤ θ ≤ π/2.

To evaluate the given iterated integral ∫∫R (1 - y²)/(9(x + y)) dA, where R is the region in the xy-plane bounded by the curves x = 0, y = 1, and 9(x + y) = 2, we can convert it to polar coordinates for easier computation.

In polar coordinates, we have x = rcos(θ) and y = rsin(θ), where r represents the distance from the origin and θ is the angle measured counter clockwise from the positive x-axis.

The integral becomes ∫∫R (1 - r²sin²(θ))/(9(rcos(θ) + rsin(θ))) r dr dθ. In the polar coordinate system, the region R corresponds to 0 ≤ r ≤ (2 - 9sin(θ))/(9cos(θ) + 9sin(θ)) and 0 ≤ θ ≤ π/2.

In the given integral, we substitute x and y with their respective polar coordinate representations. The numerator becomes 1 - r²sin²(θ), and the denominator becomes 9(rcos(θ) + rsin(θ)). Multiplying the numerator and denominator by r, we have (1 - r²sin²(θ))/(9(rcos(θ) + rsin(θ))) = (1 - r²sin²(θ))/(9r(cos(θ) + sin(θ))). We then rewrite the double integral as two separate integrals: the outer integral with respect to θ and the inner integral with respect to r. The limits of integration for θ are 0 to π/2, while the limits for r are determined by the curve 0 = (2 - 9sin(θ))/(9cos(θ) + 9sin(θ)).

We can simplify this curve to 2cos(θ) - 9sin(θ) = 9, which represents an ellipse in the xy-plane. The limits of r correspond to the radial distance within the ellipse for each value of θ. By evaluating the double integral using these limits, we can determine the result of the given iterated integral.

Learn more about Coordinates:

brainly.com/question/22261383

#SPJ11

The probability for sample mean tax is less than $7,900 is 0.1894.

μ = population mean = 8,040

σ = standard deviation = 5,000

n = amount of sample = 1,000

\(\bar x\) = sample mean = 7,900

The probability for sample mean tax can be calculated using z test formula.

P(x < 7,900) = P(z < \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n}}}\) )

= P(z < \(\frac{7,900 - 8,040}{\frac{5,000}{\sqrt{1,000}}}\))

= P(z < \(\frac{-140}{\frac{5,000}{31.622}}\))

= P(z < -0.88)

Using z table for P(z < -0.88). So,

= 0.1894

Thus, the probability is 0.1894 for sample tax mean is less than $7,900.

Learn more about probability here:

brainly.com/question/13254541

#SPJ4

Big O notation focuses on the worst-case scenario analysis, which is 0(n) for a simple search. It’s a reassurance that a simple search will never be slower than O(n) time.

Imagine that you're a teacher with a student named Ram. You want to find his records, so you use a simple search algorithm to go through your school district's database.

You know that a simple search takes O(n) times to run. This means in the worst case, you'll have to search through every single record to find Ram

After a simple search, you find that Ram records are the very first entry in the database. You don't have to look at every entry.

Did this algorithm take O(n) time Or did it take O(1) time because you found Ram records on the first try?

In this case, 0(1) is the best-case scenario – you were lucky that Ram records were at the top. But Big O notation focuses on the worst-case scenario, which is 0(n) for a simple search. It’s a reassurance that a simple search will never be slower than O(n) time.

Learn more about Big-o from

https://brainly.com/question/13257594

#SPJ4

The measure of the interior angle x is 97 degrees.

Remember that the sum of the interior angles of any triangle must be 180°.

Also remember that two adjacent angles should add to 180°.

Then the measure of the angle in the right vertex of the triangle is given by:

a + 139° = 180°

a = 180° - 139° = 41°

And now that we know two angles, we can find the third one as:

x + 41° + 42° = 180°

Solving that for x we will get:

x = 180° - 41° - 42°

x = 97°

Learn more about interior angles at:

https://brainly.com/question/24966296

#SPJ1

Answer:

0.0000004

Step-by-step explanation:

To write in standard form:

For each power of 10 bigger than 0, we add a zero at the end of the number.

For each power of 10 less than 0, we add a zero before the number(the first one before the decimal point).

In this question:

4x10^(-7)

7 zeros before the number 4, with the first before the decimal point. So

0.0000004

The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

More can be learned about absolute value functions at brainly.com/question/3381225

#SPJ1

Answer:

counters left = 160

fraction of counters left = 160/400

=2/5

a) how much cheaper = 13 ×(35.43 -15.37)

= 260.78

b) B.underestimate

Answer:

260.78

Step-by-step explanation:

2. Using proportion, the value of x = 38, the length of FC = 36 in.

3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.

The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

2. The proportion we would set up to find x is:

(x - 2) / 4 = 27 / 3

Solve for x:

3 * (x - 2) = 4 * 27

3x - 6 = 108

3x = 108 + 6

Simplifying:

3x = 114

x = 114 / 3

x = 38

Length of FC = x - 2 = 38 - 2

FC = 36 in.

3. The proportion we would set up to find x based on the angle bisector theorem is:

13 / 3x = 7 / (2x - 5)

Cross multiply:

13 * (2x - 5) = 7 * 3x

26x - 65 = 21x

26x - 21x - 65 = 0

5x - 65 = 0

5x = 65

x = 65 / 5

x = 13

Length of CD = 3x = 3(13)

CD = 39 cm

Learn more about Angle Bisector Theorem on:

https://brainly.com/question/30459648

#SPJ1

Answer: 36.576

Step-by-step explanation: The question is asking you to convert 120ft to meters

So if 94ft= 28.65 meters, then 120ft= 36.576 Meters

The length of a tennis court will be;

⇒ 36.57 meters

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The length of a basketball court = 94 feet

Which is approximately = 28.65 meters

Now,

Since, The length of a basketball court = 94 feet

Which is approximately = 28.65 meters

And, The length of a tennis court = 120 feet

So, The length of a tennis court in meters = x

⇒ x = 28.65 × 120 / 94

⇒ x = 36.57 meters

Thus, The length of a tennis court in meters = 36.57 meters

Learn more about the multiplication visit:

https://brainly.com/question/28768606

#SPJ2

Answer:

-5, -7, -8, -12

w< -4

Step-by-step explanation:

start by solvign for w

w < -4

Therefore all the values less than (but not including) -4 make the inequatliy true

so select

-5, -7, -8, -12

The equivalent inequality should be what we solved for,

w< -4

The probability of running out of water decreases.

The given problem can be solved by using the concept of the normal distribution. Normal distribution, also called Gaussian distribution, is a probability distribution that occurs naturally in many situations. In this distribution, data values cluster around a central point, and the further away a value is from the center, the less likely it is to occur. The normal distribution has two parameters: the mean (μ) and the standard deviation (σ). The mean is the center of the distribution, and the standard deviation is a measure of how spread out the distribution is. The normal distribution is symmetric about the mean. It is a continuous distribution, meaning that it can take any value between negative infinity and positive infinity. The area under the normal curve represents the probability of a random variable taking a certain value or falling within a certain range of values. The total area under the normal curve is equal to 1.
Given:
The average person drinks 3 Liters of water when hiking the Mission Peak (with a standard deviation of 1 Liter).
You are planning a hiking trip to the Mission Peak for 10 people and will bring 35 Liters of water.
What is the probability that you will run out?
We need to find the probability that the amount of water consumed by 10 people will be greater than 35 Liters. Let X be the random variable representing the amount of water consumed by each person. X is normally distributed with mean μ = 3 Liters and standard deviation σ = 1 Liter.
Then, the total amount of water consumed by 10 people is given by the sum of 10 independent identically distributed (i.i.d.) random variables:
Y = X1 + X2 + ... + X10
where X1, X2, ..., X10 are i.i.d. random variables with the same distribution as X.
The total amount of water you bring is 35 Liters. Therefore, you will run out of water if:
Y > 35
or equivalently:
(Y - μ10) / σ10 > (35 - μ10) / σ10
where μ10 = 10μ = 30 Liters and σ10 = √(10)σ = √(10) Liters.
Thus, the probability that you will run out of water is:
P(Y > 35) = P[(Y - μ10) / σ10 > (35 - μ10) / σ10]
= P(Z > (35 - μ10) / σ10)
where Z is the standard normal variable.
Using the standard normal table, we find that:
P(Z > (35 - μ10) / σ10) = P(Z > (35 - 30) / √10)
= P(Z > 1.5811)
= 0.0564 (rounded to four decimal places)
Therefore, the probability that you will run out of water when hiking the Mission Peak with 10 people is 0.0564.
What if the hiking trip will have 20 people and the amount of water you bring also doubles to 70 Liters. What is the probability you will run out?
In this case, the number of people has doubled, so the total amount of water consumed will also double. Thus, the total amount of water consumed by 20 people is given by:
Y = X1 + X2 + ... + X20
where X1, X2, ..., X20 are i.i.d. random variables with the same distribution as X.
The total amount of water you bring is 70 Liters. Therefore, you will run out of water if:
Y > 70
or equivalently:
(Y - μ20) / σ20 > (70 - μ20) / σ20
where μ20 = 20μ = 60 Liters and σ20 = √(20)σ = 2.2361 Liters.
Thus, the probability that you will run out of water is:
P(Y > 70) = P[(Y - μ20) / σ20 > (70 - μ20) / σ20]
= P(Z > (70 - μ20) / σ20)
where Z is the standard normal variable.
Using the standard normal table, we find that:
P(Z > (70 - μ20) / σ20) = P(Z > (70 - 60) / 2.2361)
= P(Z > 4.4721)
= 0 (rounded to four decimal places)
Therefore, the probability that you will run out of water when hiking the Mission Peak with 20 people is zero.

Will the probability of running out of water increase or decrease? Why?

The probability of running out of water decreases when the number of people increases and the amount of water brought doubles. This is because the total amount of water consumed increases proportionally to the number of people, but the standard deviation of the distribution of the amount of water consumed decreases proportionally to the square root of the number of people. This means that the distribution of the total amount of water consumed becomes narrower and more concentrated around the mean as the number of people increases.

for more search question probability

https://brainly.com/question/25839839

#SPJ8

Using proportions, it is found that their bill before adding the tip was of $27.48.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

They paid a 20.2% tip, hence 120.2% = 1.202 of the price x is equals to $33.03, hence the bill before the tip is found as follows:

1.202x = 33.03

x = 33.03/1.202

x = $27.48.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

3/5

Step-by-step explanation:

cos F = adjacent side/ hypotenuse

Cos F = 6/10

Cos F = 3/5

Answer:

6/10 which is 3/5

Step-by-step explanation:

Putting together the solutions from each of the equations, the 4 letter code is GFBA

From the question, we are to solve each of the linear equations to determine the 4 LETTER CODE

1. -2x + 1 = 3x + 16

Add 2x to both sides

-2x + 2x + 1 = 3x + 2x + 16

1 = 5x + 16

Subtract 16 from both sides

1 - 16 = 5x + 16 - 16

-15 = 5x

x = -15/5

x = -3

The letter that corresponds to this is G

2. 7 - 8x = 4x - 17

Add 8x to both sides

7 - 8x + 8x = 4x + 8x -17

7 = 12x - 17

Add 17 to both sides

7 + 17 = 12x - 17 + 17

24 = 12x

x = 24/12

x = 2

The letter that corresponds to this is F

3. 20 -2(x - 2) = 2x

Clear the parentheses

20 -2x + 4 = 2x

Simplify

24 -2x = 2x

Add 2x to both sides

24 - 2x + 2x = 2x + 2x

24 = 4x

x = 24/4

x = 6

The letter that corresponds to this is B

4. 5(x + 4) = 6x - 5

Clear the parentheses

5x + 20 = 6x - 5

Subtract 5x from both sides

5x - 5x + 20 = 6x - 5x - 5

20 = x - 5

Add 5 to both sides

20 + 5 = x - 5 + 5

25 = x

x = 25

The letter that corresponds to this is A

Hence,

The code is GFBA

Learn more on Solving linear equations here: https://brainly.com/question/1682776

#SPJ1

Answer:

8,000,001 and 7,999,999

Step-by-step explanation:

200^3 = 8,000,000

(200 x 200 = 40,000

40,000 x 200 = 8,000,000)

The acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

To find the acceleration of the particle at \(t = 2\) seconds, we need to differentiate the position function twice with respect to time. First, let's differentiate the position function \(s(t)\) once to find the velocity function \(v(t)\). Using the chain rule, we have:

\(\(v(t) = \frac{d}{dt}[(4t+1)^{3/2}]\)\)

To simplify the differentiation, we can rewrite the function as\(\(v(t) = (4t+1)^{3/2}\)\) . Applying the power rule, the derivative becomes:

\(\(v(t) = \frac{3}{2}(4t+1)^{1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(v(t) = 6(4t+1)^{1/2}\)\)

Next, we differentiate the velocity function \(v(t)\) to find the acceleration function \(a(t)\):

\(\(a(t) = \frac{d}{dt}[6(4t+1)^{1/2}]\)\)

Using the power rule again, we get:

\(\(a(t) = 6 \cdot \frac{1}{2}(4t+1)^{-1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(a(t) = 12(4t+1)^{-1/2}\)\)

Now we can find the acceleration at \(t = 2\) seconds by substituting \(t = 2\) into the acceleration function:

\(\(a(2) = 12(4 \cdot 2 + 1)^{-1/2}\)\)

\(\(a(2) = 12(9)^{-1/2}\)\)

Simplifying the expression, we have:

\(\(a(2) = \frac{12}{3} = 4\) cm/s²\)

Therefore, the acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

To know more about acceleration refer here:

https://brainly.com/question/12550364

#SPJ11

Answer:

x =24

Step-by-step explanation:

3(x + 4) = 4(x -3)

3x + 12 = 4x -12

add 12 to both side

3x + 24 = 4x

subtract 3x

24 = x

Given:

Number of winter coats = 2

Number of hats = 4

Number of scarves = 3

To find:

The total number of different outfit combinations.

Solution:

Number of winter coats is 2. So, the number of ways to select a winter coat from 2 coats is 2.

Number of hats is 4. So, the number of ways to select a hat from 4 hats is 4.

Number of scarves is 3. So, the number of ways to select a scarf from 3 scarves is 3.

So, the total number of ways is:

\(2\times 4\times 3=24\)

Therefore, Helen have 24 different outfit combinations.

Answer:

i can see the actual question, what is it?

In right triangles one of the angles will always be 90 degrees.

So if you had a right triangle with one right angle, a number, and a number, they always have to add up to 90 degrees as well, because a triangle is always 180 degrees

so  

Answer:

8 roses and 12 carnations.

Step-by-step explanation:

For this question, we can use substitution.

r + c = 20, so r = 20 - c.

Substitute this into the second equation, and we get (0.75)(20 - c) + 0.5 c = 12

We can expand, getting 15 - 0.75c + 0.5c = 12.

Combine like terms, and we get 0.25c = 3.

We then solve for c: 12.

Plug this back into the first equation, and we get r = 8.

There are 8 roses and 12 carnations in Denny's bouquet.

Answer:

Denny's bouquet will hold both 16 roses and 16 carnations.

Step-by-step Explanation:

0.75x16= 12

0.5x16= 8

12+8=20

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

Know more about bottleneck  here,

https://brainly.com/question/32590341

#SPJ11

The probability of meeting the manager's objectives is 0.0118.

The probability of meeting the manager's objectives if members for the team and the captain were randomly selected is very low, at 0.0118.

This is due to the fact that there are 50 basketball players in total, and the manager wants to select 5 of them, with 2 of them being seniors, 3 of them being juniors, and one of the seniors to be the captain.

This narrows the number of possibilities greatly and makes it a difficult task for the manager to fulfill.

Furthermore, the fact that the selection process is random does not help either.

This means that the manager has no control over who is chosen, and thus has to hope that the randomly selected group fulfills the desired criteria.

This makes the probability of meeting the manager's objectives even lower, as the chances of a completely random selection meeting the criteria is very low.

In conclusion,

The probability of meeting the manager's objectives if members for the team and the captain were randomly selected is very low, at 0.0118.

This shows that it is a difficult task for the manager to fulfill, and that the selection process should be carefully considered if they want to ensure that they meet their objectives.

For similar question on probability :

https://brainly.com/question/13091679

#SPJ11

Answer:

Solving for m gives:

\(m=\frac{P-50}{5}\)

which is option C in the list of possible answers

Step-by-step explanation:

Starting with the given equation, we work on using distributive property, and then on isolating the term with the variable to express:

\(P=5\,(m+10)\\P=5m+50\\P-50=5m\\\frac{P-50}{5} = m\\m=\frac{P-50}{5}\)

Answer:B

Step-by-step explanation:

B is the answer

For unbiased sample by data collection, The method to be used is Survey method.

To answer specified research questions, test hypotheses, and assess results, data collection is the act of acquiring and measuring information on variables of interest in a systematic and defined manner. All academic disciplines, including the humanities, social sciences, business, and natural and applied sciences, share the data collection component of research. Although techniques differ depending on the profession, the importance of ensuring accurate and truthful collection does not change.

The popular data collection methods are:

Survey method of data collection is to be used for collection of unbiased sample. It is so because while planning for a on-site gym for the employees, Survey conducted on the employees working would be the best method for data collection which will increase the efficiency for selection of gym hours.

To learn more about data collection visit:

https://brainly.com/question/21605027

#SPJ4

Answer: 12/15

Step-by-step explanation:

To show that the projection maps π₁: X × Y → X and π₂: X × Y → Y are open maps, we need to demonstrate that for every open set U in X × Y, the sets π₁(U) and π₂(U) are open in X and Y, respectively.

Let U be an open set in X × Y. We can write U as the union of open sets U = U₁ × U₂, where U₁ is an open set in X and U₂ is an open set in Y. Since U is open, every point (x, y) in U has an open neighborhood contained within U.

Now, consider the image of U under the projection map π₁: X × Y → X. The set π₁(U) is the collection of all x-coordinates of the points in U. For any point x' in π₁(U), there exists a point (x', y') in U. Since U is open, there exists an open neighborhood N = N₁ × N₂ of (x', y') contained within U. The projection of N onto the x-coordinate, N₁, is an open neighborhood of x' contained within π₁(U). Therefore, π₁(U) is open in X.

Similarly, for the projection map π₂: X × Y → Y, we can show that π₂(U) is open in Y. For any point y' in π₂(U), there exists a point (x', y') in U. By a similar argument as above, there exists an open neighborhood N = N₁ × N₂ of (x', y') contained within U. The projection of N onto the y-coordinate, N₂, is an open neighborhood of y' contained within π₂(U). Therefore, π₂(U) is open in Y.

Since this holds for an arbitrary open set U in X × Y, we have shown that the projection maps π₁: X × Y → X and π₂: X × Y → Y are open maps.

Learn more about Sets here -: brainly.com/question/25369230

#SPJ11